Various techniques are designed and employed in the petroleum industry for the purpose of placing sand proppant in hydraulically induced fractures to enhance oil or gas flow through a reservoir to the wellbore. Hydraulic fracturing of petroleum reservoirs typically improves fluid flow to the wellbore, thus increasing production rates and ultimate recoverable reserves. A hydraulic fracture is created by injecting a fluid down the borehole and into the targeted reservoir interval at an injection rate and pressure sufficient to cause the reservoir rock within the selected depth interval to fracture in a vertical plane passing through the wellbore. A sand proppant is typically introduced into the fracturing fluid to prevent fracture closure after completion of the treatment and to optimize fracture conductivity.
Since these fracturing techniques are performed at relatively large depths under the Earth's surface, it can be difficult to predict or determine the distribution of sand proppant throughout a network of fractures within the wellbore. Particularly in complex dynamic fracture networks (DFNs) where hundreds of fractures are interacting with each other via junctions, it can be difficult to predict or determine where the proppant being pumped into the fractures may end up within the fracture network after a certain amount of time. Previous attempts to accurately predict the effects of hydraulic fracturing processes have been lacking due to the absence of a correct, stable, and physically conservative computational method for simulating proppant laden fluid flow through a dynamic fracture network.